About the characterization of a fine line that separates generalizations and boundary-case exceptions for the Second Incompleteness Theorem under semantic tableau deduction

Our previous research showed that the semantic tableau deductive methodology of Fitting and Smullyan permits boundary-case exceptions to the second incompleteness theorem, if multiplication is viewed as a 3-way relation (rather than as a total function). It is known that tableau methodologies prove a schema of theorems verifying all instances of the law of the excluded middle. But if one promotes this schema of theorems into formalized logical axioms, then the meaning of the pronoun of ‘I’, used by our self-referencing engine, changes quite sharply. Our partial evasions of the second incompleteness theorem shall then come to a complete halt.

Subjective Scaling Elimination Test for Index-based Inherent Safety Assessment Methods

The index-based inherent safety assessment method is preferable in comparing alternative chemical process routes due to its ability to be used in the early process design stage with limited details availability of the route assessed. However, the current index-based inherent safety assessment methods available have the shortcoming of subjective scaling. The Numerical Descriptive Inherent Safety Technique (NuDIST) is an inherent safety assessment method for the research and development design stage that overcomes the shortcoming of subjective scaling by incorporating logistic functions in its scoring assignment. The aim of this paper is to verify the NuDIST method in comparison with the Prototype Index for Inherent Safety (PIIS) and Inherent Safety Index (ISI) in terms of subjective scaling elimination. The inter-boundary case subjective scaling is considered solved if the scores difference between sub-edge boundaries is small while the intra-boundary case subjective scaling is considered solved if every value in a range has different scores. The results of the subjective scaling elimination test agree that NuDIST eliminates the shortcomings of subjective scaling with positive results for both inter-boundary and intra-boundary.

Maximum Likelihood Estimation for the Fractional Vasicek Model

This paper estimates the drift parameters in the fractional Vasicek model from a continuous record of observations via maximum likelihood (ML). The asymptotic theory for the ML estimates (MLE) is established in the stationary case, the explosive case, and the boundary case for the entire range of the Hurst parameter, providing a complete treatment of asymptotic analysis. It is shown that changing the sign of the persistence parameter changes the asymptotic theory for the MLE, including the rate of convergence and the limiting distribution. It is also found that the asymptotic theory depends on the value of the Hurst parameter.

Introductory Note

In 2017 the International Court of Justice gave one judgment and made a number of orders. The judgment concerned preliminary objections in a maritime boundary case and the orders provisional measures of protection and the admissibility of certain counter-claims. These cases, although not very numerous, made a useful contribution to the development and application of internal law. In that year also no less than six new cases were begun, and one case was partially discontinued. The new cases were concerned with issues ranging from a land boundary question to compliance with two international law conventions, the revision and interpretation of a judgment, and the detention and trial of a national. The United Nations General Assembly also adopted a resolution requesting an advisory opinion. At the beginning of 2018 there were therefore seventeen cases on the Court's docket. In 2017 the Court also elected five judges to the bench in the regular triennial election.